New inquiries into bullying and harassment at Westminster still won’t investigate specific allegations.

It was announced on Tuesday that a leading barrister will conduct an independent inquiry into the treatment of MPs’ staff.

Gemma White QC has been appointed to lead the work but – following the recommendation of the House of Commons back in July – she will not investigate specific allegations against individuals or reopen past cases.

Meanwhile, the House of Lords will also establish an independent inquiry into bullying and harassment allegations.

It is also expected not to look at specific cases.

The inquiries will look at those areas not covered by a previous investigation by Dame Laura Cox, whose work was criticised for only looking at the “culture” at Westminster rather than particular accusations.

Dame Cox’s damning report, which focused on parliamentary employees rather than those working for MPs, piled pressure on senior Commons figures including Speaker John Bercow.

She judged it would be “extremely difficult” for the current administration to bring about necessary changes and found a culture of “deference, subservience, acquiescence and silence” had allowed the mistreatment of staff to thrive.

Mr Bercow has denied bullying allegations directed against him personally.

The news that parliament’s two new inquiries won’t look at individual cases or past accusations was greeted with despair by Labour shadow minister Justin Madders.

He tweeted: “When the terms of reference say ‘The inquiry will not reopen past complaints of bullying or harassment or investigate new ones… Nor will it reach conclusions or make recommendations on any individual case’ you realise all the fine words in the chamber last night count for little.”

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The FDA union, which represents public service employees, warned MPs not to use the new White inquiry as “an excuse to water down or delay the implementation” of Dame Cox’s recommendations.

The union’s assistant general secretary Amy Leversidge said: “The inquiry should also not be seen as a substitute for properly investigating past cases and staff who give evidence should have that made clear to them to avoid causing confusion.

“Dame Laura recommended lifting arbitrary restrictions on past cases, which would allow staff to bring a complaint about past behaviour and have that investigated and, if upheld, sanctioned.

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“This has been agreed by the House of Commons commission and must be implemented as soon as possible.

“We’ve seen MPs attempt to delay and water down proposals to protect staff in the past and this cannot be allowed to happen again. The time for change is now.”